hyperball_monte_carlo

hyperball_monte_carlo, an Octave code which estimates the integral of F(X) over the interior of the unit hyperball in M dimensions.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

hyperball_monte_carlo is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

hyperball_monte_carlo_test

annulus_monte_carlo an Octave code which uses the Monte Carlo method to estimate the integral of a function over the interior of a circular annulus in 2D.

ball_monte_carlo, an Octave code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit ball in 3D;

circle_monte_carlo, an Octave code which applies a Monte Carlo method to estimate the integral of a function on the circumference of the unit circle in 2D;

cube_monte_carlo, an Octave code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit cube in 3D.

disk_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of the general disk in 2D.

disk01_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of the unit disk in 2D.

disk01_quarter_monte_carlo, an Octave code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit quarter disk in 2D;

ellipse_monte_carlo an Octave code which uses the Monte Carlo method to estimate the value of integrals over the interior of an ellipse in 2D.

ellipsoid_monte_carlo an Octave code which uses the Monte Carlo method to estimate the value of integrals over the interior of an ellipsoid in M dimensions.

hyperball_integrals, an Octave code which defines test functions for integration over the interior of the unit hyperball in M dimensions.

line_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the length of the unit line in 1D.

simplex_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in M dimensions.

Reference:

1. Gerald Folland,
   How to Integrate a Polynomial Over a Sphere,
   American Mathematical Monthly,
   Volume 108, Number 5, May 2001, pages 446-448.

Source Code:

• hyperball01_monomial_integral.m, returns monomial integrals in the unit hyperball.
• hyperball01_sample.m, uniformly samples points from the unit hyperball.
• hyperball01_volume.m, returns the volume of the unit hyperball.
• monomial_value.m, evaluates a monomial.